If 2tan⁻¹(cos x) = tan⁻¹(2 cosec x), then x equals:
If 2tan⁻¹(cos x) = tan⁻¹(2 cosec x), then x equals:
- A. π/4
- B. π/3
- C. π/6
- D. π/2
Answer: A) π/4
Explanation: LHS = tan⁻¹(2cos x/(1−cos²x)) = tan⁻¹(2cos x/sin²x). RHS = tan⁻¹(2/sin x). Equating: 2cos x/sin²x = 2/sin x → cos x/sin x = 1 → cot x = 1 → x = π/4.
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